Abstract
Abstract Given a unitary operator in a finite dimensional complex vector space, its unitary contraction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the contraction allows to generate the scattering matrices of new quantum graphs from assembling of simpler graphs. The contraction of quantum channels is also defined. The implementation of the quantum gates corresponding to the contracted unitary operator is investigated, although no explicit construction is presented. The situation is different for the contraction of quantum channels for which explicit implementations are given.
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